Jordy Hiwula's ninth goal of the season, and his fourth goal in his last six games, was enough to secure a hard-fought 1-0 win for McCall's men at Cheltenham's LCI Rail Stadium.
On a difficult playing surface against fired-up opponents looking to cause an upset, City had to use all of their professionalism and experience to claim a place in the last eight of the competition.
The Bantams will now play away at Oxford United next Tuesday (24 January 2017) for a place in the Checkatrade Trophy semi-finals.
On top of the cup success, City were also boosted by a welcome return from injury for Billy Clarke, who was given the last twenty minutes or so off the substitutes' bench.
Reflecting on the game as a whole, McCall said: "We knew it would be a difficult encounter.
"It was a tough pitch to play on but we showed real attitude and desire this evening (Tuesday), especially after the disappointment of losing on Saturday (at Shrewsbury Town).
"The tackles were flying in from the first minute, and I think you could see at the end what it meant to the lads to get through.
"Cheltenham gave us a spirited performance, and we knew they would, but I feel we've dealt with the physical side of the game tonight.
"Rouven (Sattelmaier) has coped well with everything in a difficult goal-mouth and the players in front of him have won their headers and made their tackles.
"We ticked a lot of boxes in the game.
"Hans (James Hanson) managed to get some minutes under his belt, we got Billy (Clarke) back on the pitch, we got a clean sheet, and we got through.
"It was also great to see lads like Matthew Kilgallon and Rory McArdle coming into the side and playing their part. Darbs (Stephen Darby) has also done a good job for us at left back.
"Tonight was all about coming here and getting the victory. Credit to the boys, they showed more than enough desire and determination to win the game.
"We will now rest and re-energise for what will be another tough encounter at home to Millwall on Saturday."
On a pleasing night of progress for the Bantams, the only downside was a minor injury picked up Josh Cullen.
Cullen was brought on for Romain Vincelot at half time in a pre-planned move but the West Ham loanee took a whack by his knee towards the end of the game.
Following his return from injury at Cheltenham, Clarke could now feature in the Millwall game, but McCall admits Cullen will need to be assessed ahead of the encounter with the Lions.
McCall added: "It was great to see Clarkey come through the game - he puts himself in contention for Saturday (vs Millwall) now. The only slight issue was Josh Cullen getting a bang.
"He got it with five minutes to go but managed to run it off. It is only when the adrenaline wears off, however, that you can see how bad a knock is.
"He will get ice on it.
"It isn't a strain of any kind, it is a direct kick, so we are hopeful he should be fine.
"He is certainly tough enough of a player."